0=9x^4-48x^2+64

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Solution for 0=9x^4-48x^2+64 equation: 


Simplifying
0 = 9x4 + -48x2 + 64

Reorder the terms:
0 = 64 + -48x2 + 9x4

Solving
0 = 64 + -48x2 + 9x4

Solving for variable 'x'.

Combine like terms: 0 + -64 = -64
-64 + 48x2 + -9x4 = 64 + -48x2 + 9x4 + -64 + 48x2 + -9x4

Reorder the terms:
-64 + 48x2 + -9x4 = 64 + -64 + -48x2 + 48x2 + 9x4 + -9x4

Combine like terms: 64 + -64 = 0
-64 + 48x2 + -9x4 = 0 + -48x2 + 48x2 + 9x4 + -9x4
-64 + 48x2 + -9x4 = -48x2 + 48x2 + 9x4 + -9x4

Combine like terms: -48x2 + 48x2 = 0
-64 + 48x2 + -9x4 = 0 + 9x4 + -9x4
-64 + 48x2 + -9x4 = 9x4 + -9x4

Combine like terms: 9x4 + -9x4 = 0
-64 + 48x2 + -9x4 = 0

Factor a trinomial.
(-8 + 3x2)(8 + -3x2) = 0


Subproblem 1
Set the factor '(-8 + 3x2)' equal to zero and attempt to solve:

Simplifying
-8 + 3x2 = 0

Solving
-8 + 3x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + 3x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x2 = 0 + 8
3x2 = 0 + 8

Combine like terms: 0 + 8 = 8
3x2 = 8

Divide each side by '3'.
x2 = 2.666666667

Simplifying
x2 = 2.666666667

Take the square root of each side:
x = {-1.632993162, 1.632993162}

Subproblem 2
Set the factor '(8 + -3x2)' equal to zero and attempt to solve:

Simplifying
8 + -3x2 = 0

Solving
8 + -3x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -3x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x2 = 0 + -8
-3x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-3x2 = -8

Divide each side by '-3'.
x2 = 2.666666667

Simplifying
x2 = 2.666666667

Take the square root of each side:
x = {-1.632993162, 1.632993162}
Solution
x = {-1.632993162, 1.632993162, -1.632993162, 1.632993162}

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